A publicist's job is to get the attention of the public by using media sources, online methods and possibly setting up events.
A publicist gives credibility to your book, they can access media contact information quickly and have avenues to contact those media effectively. A good publicist will also have established relationships with media outlets to help garner more publicity.
A big benefit to hiring a publicity company is the media contact lists. You can set up an agreement to purchase media contact names targeted for your book. If you are very driven and want to do everything yourself, you can subscribe to a database of media contacts but expect to pay around $3,500 each year. When you consider all the hours invested and costs involved, it is usually a better deal to hire a publicity company or purchase the specific contact names from them.
In my mind, the next biggest benefit of hiring a publicist is they take all the rejection for you. Out of a list of 200 targeted contacts, I expect maybe 5 interested media contacts in a good week. It can be very discouraging to hear no 195 times every week. The publicist runs interference for you so you do not have to receive all of the rejection.